How many positive integers are there whose digits strictly increase from left to right?

(For example, 28, 13589, and 4 are all such integers. "Strictly" means no two digits can be equal, so 15668 wouldn't count.)

Guest Jul 13, 2018

#3**+1 **

How many positive integers are there whose digits strictly increase from left to right?

(For example, 28, 13589, and 4 are all such integers. "Strictly" means no two digits can be equal, so 15668 wouldn't count.)

e.g.

How many ways can 5 digits can be chosen from 9

9C5 = 126

Each of these will have only 1 number in the order needed.

So that is 126 in 5 digit numbers

Do 1 digit numbers and/or 0 count?

there are 10 of those.

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1 digit numbers 10 (includes 0)

2 digit numbers 9C2 = 36

3 digit numbers 9C3 =84

4 digit numbers 9C4=126

5 digit number 9C5 = 126

6 digit numbers 9C6=84

7 digit numbers 9C7=36

8 digit numbers 9C8=9

9 digit numbers = 1

10+36+84+126+126+84+36+9+1 = 512 ways

Melody
Jul 14, 2018